Digital wideband architectures are useful for high speed digital communication technology. Herein, the term wideband may be used to refer to bandwidths from kilohertz (KHz) to multi-gigahertz (GHz) bandwidths. Channelized architectures become necessary when the bandwidth of the signals being considered are a multiple of the speed of digital logic to process the signals. A channelizer is a circuit implementing a process, which selects a certain frequency band from a wideband input signal. The input signal typically has a higher sample rate than the sample rate of the selected channel. A typical approach to select a channel from an input signal, is to first shift the frequency of input signal by multiplying it with a complex sinusoid, then pass the signal through a low pass filter and alternatively a decimator (rate changer).
Channelized radio receivers divide an incoming radio frequency signal into plural frequency-segregated segments for performing differing signal processing of the output signal in different channels, the physical separation of hardware relating to different channels, reduction of data rate per channel, and the preclusion of cross channel interference effects, among others. In such typical channelization techniques, a frequency and a channel must be calculated and specified for each signal.
FIG. 1 shows a conventional channelized receiver. As shown, a wide band input analog signal X(t), with a frequency of, for example 4 GHz, is input to an optional anti-aliasing filter 102 to reject signals outside of the band of interest. The anti-aliasing BPF 102 filter attenuates signals outside of the spectrum of interest. A full Nyquist rate analog-to-digital converter (ADC) 104 with a sampling frequency Fs, equal to or greater than the Nyquist frequency of the input signal, samples the output of the anti-aliasing filter 102, converting the analog signal to a digital signal. The output of the ADC 104 is then channelized by a (fixed resolution) filter bank 106. The full Nyquist rate ADC 104 samples the entire signal spectrum of interest. Sampled data are separated via the fixed filter 106 bandwidth. The filter bank 106 decomposes the wideband signal into equally spaced partitions. An example of a channelizing filter bank is a polyphaser, which splits an input signal into a given number N (mostly a power of 2) of equidistant sub-bands. These sub-bands are then subsampled by a factor of N, so they are critically sampled.
Some approaches use the above-described conventional channelized receiver followed by compressive sensing to unwrap the aliased narrow-band spectrum resulting from under sampling. This approach works well for detection of sparse (narrow-band) signals across the wide band of interest. Compressive sensing takes advantage of the fact that a signal can be sparsely represented in a transformed domain (e.g., when a sinusoidal or cosine signal is transformed to Fourier domain by applying the Fourier transform, it can be represented by just two coefficients.). Many signals can be sparsely represented in a transformed domain and thus contain many coefficients in that domain close to or equal to zero (e.g., Fourier or Wavelet). The approach typically starts with taking a weighted linear combination of samples (compressive measurements) using a set of basis functions that are different from the set of basis functions in which the signal is known to be sparse.
A critically sampled channelizer contains spectrum gaps (blind spots), which are the energy differences between the ground state and first excited state of the channelizer. If any of the signal samples fall within these spectrum gaps, that sample cannot be detected and recovered. To reduce these gaps, some approaches oversample the input signal to substantially increase the frequency of the samples to fill the gaps between the channels in the channelized spectrum and therefore minimize the chances of data being lost in the spectrum gaps. This way, signals at the channel boundaries are detected in multiple channels. However, these oversampling approaches create substantially more data which takes more processing power and memory space resulting in more complex and expensive channelizers. Similarly, critically sampled or undersampled channelizers use less resources, but also have gaps in the spectrum, which may also lead to loss of data.